## THE FARMER-BEATTIE SITING CRITERION

The probability per annum P(C) that a reactor accident releases C curies[60] of radioiodides is derived from the usual general form [173] as

Equations (4.4) and (4.9) reveal the physical dimension of f (C) as (years)-1, so its ordinates are often referred to as (years)-1 or those of [f (C)]—1 as years. Substitution of equation (4.9) into (4.5) yields

C2

[ f (C)/2.303C]dC

C1

If C is the median point between Ci and C2 lying on f (C) with

Ci = СЛ/Ї0 and C2 = ЫЮ then equation (4.10) evaluates [157] as

pjWlO) — Р^/л/Ш) = af (C) where a = 1.576 (4.11)

Reactor safety assessments provide a spectrum of Severe Accidents with varying ground-level concentrations of the principal radioiodides. A straight line with gradient =—1 can then be drawn in log10 P(C) and log10C coordinates to represent an acceptable upper bound in terms of the criteria (4.2) and (4.3) on page 81, for all the investigated cases. Though points on such a line correspond to equal risk as defined by equation (4.3), they do not represent equal fatalities because lower absorptions favor our bodies’ natural repair processes and curative surgery. Also because adverse public concern and reaction increases with an increasing hazard, an arbitrary 3/2 weighting is adopted for the bounding line [157].

F(C) = AC-3/2 for C > 1 kCi (4.12)

Over the years worldwide commercial reactor operations have accumulated several thousand operational years. Within this context, what constitutes a publically acceptable risk? Farmer [157] argues that the release of less than 1 kCi in 1000 years should be deemed reasonable in order to restrict lost power production and diagnostic investigations to sensible proportions. Because the number of Severe Accidents is obviously a discrete variable and because such accidents are engineered to be rare events, statistical characterization by a Poissonian distribution [173] is the most appropriate. Accordingly, the probability of n iodide releases of 1 kCi in T years is in general given by

P(n)= — — exp (—vT) (4.13)

n!

where v is the expected number of events per year. For an expected release of just one 1 kCi in 1000 years, it follows that

vT = 1

so

P(1) = 0.37 and P(0) = 0.37

Farmer and Beattie [157] derive sufficiently close values of 0.33 on the less certain basis of a Normal distribution to justify the smooth transition from equation (4.10) to

F(C) = 10“2 for C950 Ci (4.14)

in Figure 4.2, which is called the Farmer Curve. Its sufficiency as an upper probability bound for an acceptable radioiodide release in the United Kingdom, Severe Accidents are now considered in the context of criteria (4.2) and (4.3) on page 81.

If h(N) denotes the usual form of probability density function for the number of thyroid cancers presenting as a result of a radioiodide releases, then similar to the above

and on the more convenient logarithmic scales

«So= H(N) with h(N)=H(N)/2-303N

with: n2

[H(N )/2.303N ]dN

N1

Though the Lebesgue Measure [114,173] is strictly required to accommodate the probability density and distribution functions of both discrete and continuous variables, d-functions [124] and Riemann Integration provide a more accessible and tangible appreciation of the above. Due to the complex natures of weather patterns and population density an evaluation of equation (4.17) is intractable in practice, so some simplifying yet conservative approximations are necessary. In this respect UK statistical data on wind velocities[61] and Pasquill’s six weather categories for aerosol dispersion are averaged to produce a wind factor W from which the dose D rem from an emission of C Curies is described by

D = WC/r1-5 (4.18)

where r is the radial distance from a source. The expected number N of thyroid cancer patients presenting out of Q who receive this dose is then approximated by

N = QBD for D > 10 rem

= 0 for D < 10 rem (4Л9)

where B = 15 x 10-6 per rem is the mean of age-dependent values[62] specified by the International Committee on Radiological Protection

[174]. A representative population of 4 million around an AGR is assumed to be uniformly distributed in an annulus of radii 1/2 and 10 miles. The inner radius indicates that few homes are usually near a site boundary, and the outer limit an intrinsically decreasing dose with distance (r). Wind directions are quantized into 30° sectors which are also the limits of aerosol dispersion.

With the above conservative assumptions the expected increase in thyroid cancer presentations after a UK Severe Accident can be inferred. Calculations with the STRAP code [175] for a 10kCi release give a total individual dose of 2.2 x 106 man-rem for the above population, and therefore 33 presenting cases per million (i. e., 15 x 2.2). However, for a reactor satisfying Farmer’s Curve in Figure 4.2 the probability of this event is no greater than 0.66 x 10“4 per operating year, so the expected annual number of presenting cases is no greater than 0.0022 per million. Now the UK population in 2011 was around 62 million so the natural annual fatalities from the disease is derived from Table 4.1 as 5.7 per million, which thanks to surgery is an 80-90% reduction of the 1770 per million annual presentations. This calculation and others by Farmer and Beattie show that the additional annual risk to the local population from a Severe Accident with a UK reactor is exceedingly small by comparison with the natural cause: criterion (4.3).

Minimizing individual risk often figures significantly in public health criteria. With a 10 kCi release of radio-iodides the probable dose to a child at 1000 yards (914m) is computed [175] as 400rem. If this dose were actually received, the expectation of developing a thyroid cancer would be 6 x x 400 . Ignoring prevailing

wind effects, the assumed 30° sectors of aerosol dispersion imply only a 1 in 12 chances that this dose is actually received, so the risk reduces to 5 x 10“4. Moreover, the probability of this event for a site satisfying Farmer’s Curve is no greater than 0.66 x 10“4 per operating year, so the expectation of thyroid cancer for this child is just 3 x 10“8 per annum. The aggregate risk for a reactor with 4 or 5 mutually exclusive [173] releases on or close to the bounding curve is evaluated as approximately 1 x 10“7 per operating year. Thus subject to meeting the Farmer — Beattie constraint the additional annual expectation of developing thyroid cancer for an individual most at risk is orders of magnitude less than the natural incidence: criterion (4.2). Table 4.1 reveals that the self-imposed risk of death from a road accident or tobacco smoking is decades greater still.

The above analysis enables the Three Mile Island reactor accident to be placed in perspective. Although its fuel contained between 3 to 5 million curies of radioiodides [104], almost all were dissolved in the water or vapor within the sump and auxiliary building, and just 16 curies were released into the atmosphere [66]. Earlier destructive tests within small experimental reactors confirm the effectiveness of water or sodium coolants in reducing atmospheric releases of fission products [104]. The maximum additional individual exposure at TMI and that to the surrounding population have been estimated [66] at 80 m rem and 1.5 m rem respectively, whilst the natural background radiation is about 100 m rem. In this context the natural background radiation in the granite city of Aberdeen is some three times that of London which is built on Mesozoic geology: yet there is no statistically significant difference in attributable cancers for the two populations.[63]